Prediction of the Bending Strength of a Composite Steel Beam–Slab Member Filled with Recycled Concrete

This study investigated the structural behavior of a beam–slab member fabricated using a steel C-Purlins beam carrying a profile steel sheet slab covered by a dry board sheet filled with recycled aggregate concrete, called a CBPDS member. This concept was developed to reduce the cost and self-weight of the composite beam–slab system; it replaces the hot-rolled steel I-beam with a steel C-Purlins section, which is easier to fabricate and weighs less. For this purpose, six full-scale CBPDS specimens were tested under four-point static bending. This study investigated the effect of using double C-Purlins beams face-to-face as connected or separated sections and the effect of using concrete material that contains different recycled aggregates to replace raw aggregates. Test results confirmed that using double C-Purlins beams with a face-to-face configuration achieved better concrete confinement behavior than a separate configuration did; specifically, a higher bending capacity and ductility index by about +10.7% and +15.7%, respectively. Generally, the overall bending behavior of the tested specimens was not significantly affected when the infill concrete’s raw aggregates were replaced with 50% and 100% recycled aggregates; however, their bending capacities were reduced, at −8.0% and −11.6%, respectively, compared to the control specimen (0% recycled aggregates). Furthermore, a new theoretical model developed during this study to predict the nominal bending strength of the suggested CBPDS member showed acceptable mean value (0.970) and standard deviation (3.6%) compared with the corresponding test results.


Introduction
The building industry is continually developing new composite structural members to replace conventional members (reinforced concrete, steel, and wood timber) for a variety of reasons, including cost, availability of materials in the market, ease of fabrication, higher strength, better durability, and environment effects [1]. In 1989, Wright et al. [2] studied the composite structural performance of a profiled steel sheet deck slab system with cementitious dry board sheet, usually known as a "PSSDB or PDS system". Later, several researchers tested the PSSDB system adopted in the floors, walls, and roofs of residential and commercial buildings [3][4][5][6]. The influence of filling a one-way PSSDB slab with geopolymer and normal concrete was experimentally investigated [7,8]. In addition, Al-Shaikhli et al. [9,10] studied the bending behavior of concrete-filled PSSDB slabs using the two-way slab concept. However, PSSDB deck slabs (with/without infill concrete) are in addition to the self-tapping steel screws (DS-FH432) that provid nailing the concrete core of the CFST beams (see Figures 2 and 3). D casting process, a vibrating device was used to better distribute infil specimen's sections (see Figure 4). Following this, the PSS deck slab w sheets that were fixed in place using self-tapping screws (DS-HW640)  points) was expected to acting as a shear connector, to further improve the connection behavior between the slab (PDS) and beam (CB) parts of this composite CBPDS specimen, in addition to the self-tapping steel screws (DS-FH432) that provided extra length for nailing the concrete core of the CFST beams (see Figures 2 and 3). During the concrete casting process, a vibrating device was used to better distribute infill material inside the specimen's sections (see Figure 4). Following this, the PSS deck slab was covered with DB sheets that were fixed in place using self-tapping screws (DS-HW640).     This study adopted a new technique for filling CBPDS specimens with concrete that provided several equally distributed (40 × 80 mm at 340 mm c/c) openings along the contact surface between the deck slab and the beam, as shown in Figure 4. This technique was considered more practical and easier to accomplish at the construction site compared to the existing method of pouring concrete inside the CFST beams by placing them vertically until they set [21,47]. Generally, concrete located at these openings (interlock points) was expected to acting as a shear connector, to further improve the connection behavior between the slab (PDS) and beam (CB) parts of this composite CBPDS specimen, in addition to the self-tapping steel screws (DS-FH432) that provided extra length for nailing the concrete core of the CFST beams (see Figures 2 and 3). During the concrete casting process, a vibrating device was used to better distribute infill material inside the specimen's sections (see Figure 4). Following this, the PSS deck slab was covered with DB sheets that were fixed in place using self-tapping screws (DS-HW640).

Material Properties
Three different concrete mixtures were prepared, each containing a different amount of recycled aggregates (0%, MC0; 50%, MC50; and 100%, MC100) which were replaced by volume with raw fine and raw coarse aggregates. The concrete mixtures were mainly prepared using Malaysian Portland cement (MS EN 197-1 CEM II/B-L 32.5N), washed sand (density, 1570 kg/m 3 ), and crushed limestone coarse aggregates (density, 1498 kg/m 3 ). A high water/cement ratio (0.5) was used to increase the concrete mixture's workability while it was poured inside the CBPDS specimens. In this study, combinations of four different waste materials were used as recycled aggregates (EPS, CCA, CRA, and FGA), as shown in Figure 5. Sieve analysis was performed in the laboratory for three recycled materials, as shown in Figure 6. The densities of these recycled aggregates were 1278 kg/m 3 for the CCA, 9.5 kg/m 3 for the EPS, 600 kg/m 3 for the CRA, and 1220 kg/m 3 for the FGA. Table 2 presents the proportions of these concrete mixtures. After 28 days, three cubes (100 mm) were taken from each mixture and tested in accordance with BS1881-Part116 1983. In general, at the preliminary lab work stage, five concrete mixtures that contain different combinations of recycled aggregates were suggested. Then, one mixture was chosen to apply as infill recycled concrete material for the investigated CBPDS specimen, specifically the mixture with optimal content of recycled aggregates and better concrete strength compared to normal concrete NC.
concrete strength compared to normal concrete NC.
In addition, three steel coupons were prepared, using steel PSS and C-Purlins, and tested in accordance with ASTM E8/E8M-2009. This study used the same Primaflex DB sheet that was used in [7,9,10]. Table 3 presents the properties of these materials (C-Purlins, PSS, DB, and concrete mixtures). Lastly, two types of self-tapping steel screw were used to connect the parts of the CBPDS specimens, which are DS-and DS-FW640 [7,9,10].

Test Setup
All CBPDS specimens were tested as a simply supported beam, using the test setup shown in Figure 7, all dimensions in mm. During the loading test, three LVDTs, positioned under the specimens, recorded their vertical deflection, and five strain gauges (SG), located at the mid-spans, measured changes in the longitudinal strain values of the C-Purlin beams, PSS slabs, and DB sheets. The load was applied at two points and was increased using a continuous increment (6-8 kN/min). The deflection, load, and strain values were collected and saved in a PC using a data logger device.   30 20 20 1950 In addition, three steel coupons were prepared, using steel PSS and C-Purlins, and tested in accordance with ASTM E8/E8M-2009. This study used the same Primaflex DB sheet that was used in [7,9,10]. Table 3 presents the properties of these materials (C-Purlins, PSS, DB, and concrete mixtures). Lastly, two types of self-tapping steel screw were used to connect the parts of the CBPDS specimens, which are DS-and DS-FW640 [7,9,10].

Test Setup
All CBPDS specimens were tested as a simply supported beam, using the test setup shown in Figure 7, all dimensions in mm. During the loading test, three LVDTs, positioned under the specimens, recorded their vertical deflection, and five strain gauges (SG), located at the mid-spans, measured changes in the longitudinal strain values of the C-Purlin beams, PSS slabs, and DB sheets. The load was applied at two points and was increased using a continuous increment (6-8 kN/min). The deflection, load, and strain values were collected and saved in a PC using a data logger device.

Typical Failure Mode
The tested CBPDS specimens showed similar bending behavior with compressive stresses at the top flange of the slab part (PDS), and tension stresses at bottom flanges of the C-Purlins beam part (CB). Generally, this performance was observed for all specimens regardless of the recycled aggregate composition of their concrete cores (0%, 50%, and 100%), and for both C-Purlins beam configurations. The specimens with double C-Purlins filled with the highest percentages of recycled aggregates (specimens CBPDS-DF100 and CBPDS-DS100) showed a typical steel outward buckling failure similar to the corresponding control specimens CBPDS-DF0 and CBPDS-DS0 (0% recycled aggregates), as compared in Figure 8. Tube buckling occurred at the top flanges of C-Purlins when the loading test passing 85% of the specimens' ultimate bending capacity. In addition, none of the DB sheets or infill concrete materials inside the PSS slab recorded any crushing failure, as shown in Figure 9. This was due to the influence of infill concrete materials

Typical Failure Mode
The tested CBPDS specimens showed similar bending behavior with compressive stresses at the top flange of the slab part (PDS), and tension stresses at bottom flanges of the C-Purlins beam part (CB). Generally, this performance was observed for all specimens regardless of the recycled aggregate composition of their concrete cores (0%, 50%, and 100%), and for both C-Purlins beam configurations. The specimens with double C-Purlins filled with the highest percentages of recycled aggregates (specimens CBPDS-DF100 and CBPDS-DS100) showed a typical steel outward buckling failure similar to the corresponding control specimens CBPDS-DF0 and CBPDS-DS0 (0% recycled aggregates), as compared in Figure 8. Tube buckling occurred at the top flanges of C-Purlins when the loading test passing 85% of the specimens' ultimate bending capacity. In addition, none of the DB sheets or infill concrete materials inside the PSS slab recorded any crushing failure, as shown in Figure 9. This was due to the influence of infill concrete materials inside the PDS part, even with high percentages of recycled aggregates (50% and 100%), which is considered an important contribution to this CBPDS system.  In addition, the same failure mode was observed for specimens CBPDS-DS0, CBPDS-DS50, and CBPDS-DS100 (double separate beam). However, the concrete core of these beams experienced earlier cracking failure than those with face-to-face connections; the latter configuration achieved better concrete confinement behavior, as it was fabricated in a tube shape [21,45]. Generally, these cracks started when about 70-75% of the specimens' ultimate bending capacity was achieved, and gradually increased with increases in the loading test, as shown for specimen CBPDS-DS100 in Figure 10. Furthermore, no concrete slipping failures from the C-Purlins or PSS sections were recorded for any of the tested specimens, even at the extreme bending stage. This perfect bonding behavior between the concrete core and the steel section of CBPDS specimens was achieved due to the openings provided to casting the concrete and the embedded length of self-tapping screws used to fix the PSS to C-the Purlins beams. This behavior was recorded for all specimens, even those containing 100% recycled aggregates with double separate C-Purlins beams. All specimens showed a typical deflection behavior similar to the half-sine curve ( Figure 11).

Bending Behavior and Strength
Generally, CBPDS specimens' bending behavior was expressed as a moment-deflection relationship, as shown in Figure 12. Regardless of the recycled aggregates content of infill concrete material (0%, 50%, or 100%) and the C-Purlins' configuration (face-to-face or separate connections), all specimens showed elastic behavior at the early loading stage (at 50-60% of each specimen's ultimate capacity). Next, these curves showed an elastic-plastic behavior with continuously dropping slopes until the peak points were achieved at the curve. After that, their moment-deflection curves rapidly decreased due to the increased steel buckling of the PSS slabs and C-Purlins beams as well as increasing concrete cracks inside the beams at the shear span distance. However, the specimens containing 50% and 100% recycled aggregates (CBPDS-DF50, CBPDS-DS50, CBPDS-DF100, and CBPDS-DS100) exhibited slightly lower bending behavior than their corresponding control specimens (CBPDS-DF0 and CBPDS-DS0), specifically at the plastic loading stage, due to the lower compressive strength of their concrete mixtures (MC50 and MC100).  The ultimate bending strengths (M u ) obtained at the peak values of all tested specimens' moment-deflection curves are recorded in Table 1. In addition, Figure 13 compares the M u values of the CBPDS specimens based on their infill concrete mixture (MC0, MC50, or MC100) and according to their C-Purlins beam configuration (CBPDS-DF and CBPDS-DS). Generally, regardless of the C-Purlins connection type, specimens' M u values decreased as the recycled aggregate content increased, which is logical, as the concrete's compressive strength usually decreased accordingly, as shown earlier in Table 2. For example, the M u value decreased approximately 7% when 50% of the raw aggregate was replaced with recycled aggregates, from 51.5 kN.m for specimen CBPDS-DF0 (control specimen) to 47.7 kN.m for specimen CBPDS-DF50. The M u value decreased approximately 11% (46.1 kN.m) when 100% recycled aggregate was used (specimen CBPDS-DF100). Therefore, it can be concluding that replacing 100% of the raw aggregate with a combination of recycled aggregates reduced the suggested composite beam-slab specimens' concrete cores' self-weight by approximately 15%; their M u values decreased approximately 9-11% with little effect on overall bending behavior.
(face-to-face or separate connections), all specimens showed elastic behavior at the early loading stage (at 50%-60% of each specimen's ultimate capacity). Next, these curves showed an elastic-plastic behavior with continuously dropping slopes until the peak points were achieved at the curve. After that, their moment-deflection curves rapidly decreased due to the increased steel buckling of the PSS slabs and C-Purlins beams as well as increasing concrete cracks inside the beams at the shear span distance. However, the specimens containing 50% and 100% recycled aggregates (CBPDS-DF50, CBPDS-DS50, CBPDS-DF100, and CBPDS-DS100) exhibited slightly lower bending behavior than their corresponding control specimens (CBPDS-DF0 and CBPDS-DS0), specifically at the plastic loading stage, due to the lower compressive strength of their concrete mixtures (MC50 and MC100). The ultimate bending strengths (Mu) obtained at the peak values of all tested specimens' moment-deflection curves are recorded in Table 1. In addition, Figure 13 compares the Mu values of the CBPDS specimens based on their infill concrete mixture (MC0, MC50, or MC100) and according to their C-Purlins beam configuration (CBPDS-DF and CBPDS-DS). Generally, regardless of the C-Purlins connection type, specimens' Mu values decreased as the recycled aggregate content increased, which is logical, as the concrete's compressive strength usually decreased accordingly, as shown earlier in Table  2. For example, the Mu value decreased approximately 7% when 50% of the raw aggregate was replaced with recycled aggregates, from 51.5 kN.m for specimen CBPDS-DF0 (control specimen) to 47.7 kN.m for specimen CBPDS-DF50. The Mu value decreased approximately 11% (46.1 kN.m) when 100% recycled aggregate was used (specimen CBPDS-DF100). Therefore, it can be concluding that replacing 100% of the raw aggregate with a combination of recycled aggregates reduced the suggested composite beam-slab specimens' concrete cores' self-weight by approximately 15%; their Mu values decreased approximately 9%-11% with little effect on overall bending behavior.  Figure 14 presents specimens' moment-strain relationships, specifically for specimens with 0% and 100% recycled aggregates. In general, the SG1 and SG2 strain gauges measured negative strain values; this confirmed that the top fibers of specimens were subjected to compression stress due to the high bending stress at their mid-spans. In contrast, the SG5 strain gauge (fixed at the beams' bottom flanges) showed continuous increases in positive strain values. The SG3, located at the connection surface between the C-Purlins and PSS deck slab, first measured marginally negative strain values, and then measured positive strain values when loads reached 90%-97% of the specimens' ultimate strength. This performance indicated that each CBPDS specimen's neutral axis (NA) was within the top quarter of its beam's cross-section; then, the NA moved upward until it was slightly above the beam-slab connection level and became slightly above the bottom flange of the PSS (see Figure 14). Moreover, the negative strain values of SG2 (fixed at PSS' top flanges) did not reach the yielding limit even at the extreme loading stage indicating  Figure 14 presents specimens' moment-strain relationships, specifically for specimens with 0% and 100% recycled aggregates. In general, the SG1 and SG2 strain gauges measured negative strain values; this confirmed that the top fibers of specimens were subjected to compression stress due to the high bending stress at their mid-spans. In contrast, the SG5 strain gauge (fixed at the beams' bottom flanges) showed continuous increases in positive strain values. The SG3, located at the connection surface between the C-Purlins and PSS deck slab, first measured marginally negative strain values, and then measured positive strain values when loads reached 90-97% of the specimens' ultimate strength. This performance indicated that each CBPDS specimen's neutral axis (NA) was within the top quarter of its beam's cross-section; then, the NA moved upward until it was slightly above the beam-slab connection level and became slightly above the bottom flange of the PSS (see Figure 14). Moreover, the negative strain values of SG2 (fixed at PSS' top flanges) did not reach the yielding limit even at the extreme loading stage indicating that the compression strength of specimens' PSS slabs did not reach their yielding limits. In contrast, SG5 (fixed at the C-Purlin's bottom flange) readings indicated that steel C-Purlins' tensile strengths started to achieve their yielding limits when the bending moment reached approximately 85-90% of the specimens' ultimate bending strength. Lastly, increasing the recycled aggregate content in the concrete to 100% had no effect on the moment-strain relationships of CBPDS specimens. specimens with 0% and 100% recycled aggregates. In general, the SG1 and SG2 strain gauges measured negative strain values; this confirmed that the top fibers of specimens were subjected to compression stress due to the high bending stress at their mid-spans. In contrast, the SG5 strain gauge (fixed at the beams' bottom flanges) showed continuous increases in positive strain values. The SG3, located at the connection surface between the C-Purlins and PSS deck slab, first measured marginally negative strain values, and then measured positive strain values when loads reached 90%-97% of the specimens' ultimate strength. This performance indicated that each CBPDS specimen's neutral axis (NA) was within the top quarter of its beam's cross-section; then, the NA moved upward until it was slightly above the beam-slab connection level and became slightly above the bottom flange of the PSS (see Figure 14). Moreover, the negative strain values of SG2 (fixed at PSS' top flanges) did not reach the yielding limit even at the extreme loading stage indicating that the compression strength of specimens' PSS slabs did not reach their yielding limits. In contrast, SG5 (fixed at the C-Purlin's bottom flange) readings indicated that steel C-Purlins' tensile strengths started to achieve their yielding limits when the bending moment reached approximately 85%-90% of the specimens' ultimate bending strength. Lastly, increasing the recycled aggregate content in the concrete to 100% had no effect on the moment-strain relationships of CBPDS specimens.

Ductility Index
Typically, for all tested specimens, the DI value was estimated from the deflection ratio at the ultimate bending limit (δu) to that at the yielding limit (δy) [48], as illustrated in Figure 15. Specimens' DI indices are compared in Figure 16 with reference to their C-Purlins connection type (CBPDS-DF or CBPDS-DS). Generally, regardless of beam configuration, the highest DI value was achieved by control specimens with 0% recycled aggregate content; this value gradually decreased as recycled aggregate content increased. For example, control specimen CBPDS-DF0′s DI value was approximately 4.4, compared to DI values of 4.1 (−7.0%) and 3.4 (−22%) when specimens' infill concrete materials contained 50% and 100% recycled aggregates, respectively. Generally, specimens with double separate C-Purlins beams (CBPDS-DS) showed similar performance to specimens with face-to-face connection beams (CBPDS-DF), but with slightly lower DI values, as the specimens with face-to-face beam configurations achieved better concrete confinement, which led to improved bending performance.

Ductility Index
Typically, for all tested specimens, the DI value was estimated from the deflection ratio at the ultimate bending limit (δ u ) to that at the yielding limit (δ y ) [48], as illustrated in Figure 15. Specimens' DI indices are compared in Figure 16 with reference to their C-Purlins connection type (CBPDS-DF or CBPDS-DS). Generally, regardless of beam configuration, the highest DI value was achieved by control specimens with 0% recycled aggregate content; this value gradually decreased as recycled aggregate content increased. For example, control specimen CBPDS-DF0 s DI value was approximately 4.4, compared to DI values of 4.1 (−7.0%) and 3.4 (−22%) when specimens' infill concrete materials contained 50% and 100% recycled aggregates, respectively. Generally, specimens with double separate C-Purlins beams (CBPDS-DS) showed similar performance to specimens with face-toface connection beams (CBPDS-DF), but with slightly lower DI values, as the specimens with face-to-face beam configurations achieved better concrete confinement, which led to improved bending performance. ratio at the ultimate bending limit (δu) to that at the yielding limit (δy) [48], as illustrated in Figure 15. Specimens' DI indices are compared in Figure 16 with reference to their C-Purlins connection type (CBPDS-DF or CBPDS-DS). Generally, regardless of beam configuration, the highest DI value was achieved by control specimens with 0% recycled aggregate content; this value gradually decreased as recycled aggregate content increased. For example, control specimen CBPDS-DF0′s DI value was approximately 4.4, compared to DI values of 4.1 (−7.0%) and 3.4 (−22%) when specimens' infill concrete materials contained 50% and 100% recycled aggregates, respectively. Generally, specimens with double separate C-Purlins beams (CBPDS-DS) showed similar performance to specimens with face-to-face connection beams (CBPDS-DF), but with slightly lower DI values, as the specimens with face-to-face beam configurations achieved better concrete confinement, which led to improved bending performance.

Theoretical Model Development
The steel tube members were classified as either slender, non-compact (semicompact), or compact sections, according to how they buckle under compression stress [20,49]. Specifically, the AISC-2010 standard [50] classifies rectangular CFST members. The suggested CBPDS specimens' beams were fabricated using double C-Purlins members filled with concrete materials, and classified as slender sections [20,21]. The PSS deck slabs in this composite specimen were also classified as slender sections, as the PSS sections were thin relative to the flat distance of their cross-sections, which was evident when the PSS' top flanges buckled under compression stress (at mid-span distance due to their bending behavior). However, to date, there is no analytical model that can predict the nominal bending capacity (Mn) of the investigated composite beam-slab member (CFST beam carrying a PSSDB/PDS slab). Therefore, in this study, a new theoretical model was developed using the stress block theory, as shown in Figure 17. The main assumptions adopted in the development of this model are as follows: 1. This model is limited to the concrete-filled composite CBPDS specimens prepared with rectangular steel tube beams and PSS deck slabs covered with dry board (DB) sheet subjected to static bending loads. 2. The concrete cores achieved full interaction with the steel tube beams and PSS deck slabs, as no slip failures were recorded for the tested specimens (see Section 3.1). 3. The steel tube beams achieved full interaction with the PSS slabs, as no

Theoretical Model Development
The steel tube members were classified as either slender, non-compact (semi-compact), or compact sections, according to how they buckle under compression stress [20,49]. Specifically, the AISC-2010 standard [50] classifies rectangular CFST members. The suggested CBPDS specimens' beams were fabricated using double C-Purlins members filled with concrete materials, and classified as slender sections [20,21]. The PSS deck slabs in this composite specimen were also classified as slender sections, as the PSS sections were thin relative to the flat distance of their cross-sections, which was evident when the PSS' top flanges buckled under compression stress (at mid-span distance due to their bending behavior). However, to date, there is no analytical model that can predict the nominal bending capacity (M n ) of the investigated composite beam-slab member (CFST beam carrying a PSSDB/PDS slab). Therefore, in this study, a new theoretical model was developed using the stress block theory, as shown in Figure 17. The main assumptions adopted in the development of this model are as follows:

1.
This model is limited to the concrete-filled composite CBPDS specimens prepared with rectangular steel tube beams and PSS deck slabs covered with dry board (DB) sheet subjected to static bending loads.

2.
The concrete cores achieved full interaction with the steel tube beams and PSS deck slabs, as no slip failures were recorded for the tested specimens (see Section 3.1).

3.
The steel tube beams achieved full interaction with the PSS slabs, as no horizontal/vertical separations were recorded for the tested specimens (see Section 3.1).

4.
The effects of C-Purlins lips were ignored. 5.
The effects of the infill concrete section below the NA was ignored, as it was subjected to tension stress and faced cracking failure [20]. 6.
As both the steel tube beam and PSS slab are slender sections, a pure elastic behavior has been assumed for these sections, which is limited to f y-CB at the C-Purlins' bottom flange (maximum tension stress) [20], as the tensile strain values shown in Figure 14 (SG5). Furthermore, the PSSs' top flange (maximum compression stress) is limited to the buckling stress (f s-pss ), as it has not reached the yield limit (see SG2 in Figure 14). Thus, the stress value of f s-pss is estimated via liner interpolation with the value of f y-CB . 7.
A lower compression stress equal to 0.8f cu and 0.8f u-DB is adopted for the concretefilled PSS slab and DB sheet, respectively, as no crush failures were recorded for these two sections until the end of specimen tests (as previously discussed in Section 3.1 and shown in Figure 9). 8.
To simplify this model, the position of NA (y n ) is assumed to be located at the beamslab connection level (connection level of C-Purlins with PSS), as previously discussed in Section 3.3, based on the readings of strain gauge SG3, as highlighted in Figure 14. 9.
Lastly, for design purposes, reduction factors (Ø) equal to 0.8 and 0.7 are suggested for predicting the M n values of CBPDS specimens with double face-to-face C-Purlins beam and double separate beams, respectively.
Materials 2023, 16, x FOR PEER REVIEW 14 of 18 discussed in Section 3.3, based on the readings of strain gauge SG3, as highlighted in Figure 14. 9. Lastly, for design purposes, reduction factors (Ø) equal to 0.8 and 0.7 are suggested for predicting the Mn values of CBPDS specimens with double face-to-face C-Purlins beam and double separate beams, respectively.
Based on the above assumptions and details presented in Figure 17, the forces over the CBPDS specimens' sections have been estimated to form the final expression of the newly suggested theoretical model, summarized as follows:  Table 1 and Figure 18. A lower estimate was achieved using this developed model with a sufficient mean value and standard deviation of 0.970 and 3.6%, respectively.   Based on the above assumptions and details presented in Figure 17, the forces over the CBPDS specimens' sections have been estimated to form the final expression of the newly suggested theoretical model, summarized as follows: M n = Ø (F CB-flange . Y CB-flange + F CB-web . Y CB-web + F PSS . Y PSS + F con . Y con + F DB . Y DB ) (1) where the detail of forces is as follows, The M n values of the investigated CBPDS specimens are predicted using the new analytical model and compared with those obtained from the corresponding test results in Table 1 and Figure 18. A lower estimate was achieved using this developed model with a sufficient mean value and standard deviation of 0.970 and 3.6%, respectively.

YDB
= the distance of FDB from the N.A = DPSS + 1/2.tDB Ø = 0.8 for CBPDS specimens (double face-to-face C-purlins beam) 0.7 for CBPDS specimens (double separate C-purlins beam) The Mn values of the investigated CBPDS specimens are predicted using the new analytical model and compared with those obtained from the corresponding test results in Table 1 and Figure 18. A lower estimate was achieved using this developed model with a sufficient mean value and standard deviation of 0.970 and 3.6%, respectively.

Conclusions
The conclusions are summarized as follows: Filling CBPDS specimens with infill material containing 50% and 100% of recycled aggregate had little effect on their flexural behavior. Thus, using a combination of different recycled aggregates (EPS, CCA, CRA, and FGA) in the specimens' concrete cores achieved a sufficient contribution, by reducing their self-weight approximately 15-18% and using less raw aggregate, which was considered an environmental improvement.
Increasing the recycled aggregate content of the CBPDS specimens' concrete materials to 50% and 100% reduced their ultimate bending strength by approximately 7-11% compared to the control specimen, due to reductions in their concrete compressive strengths. However, the specimen beams with double separate C-Purlins sections had slightly lower bending capacities than those with face-to-face connections. For example, the specimen with face-to-face C-Purlins beam and filled with 100% recycled concrete materials (CBPDS-DF100) achieved bending capacity equal to 46.1 kN.m, where this capacity reduced to 43 kN.m only when the C-Purlins beams were separated (CBPDS-DS100). Accordingly, the CBPDS specimens' ductility indexes were reduced with increases of recycled aggregate content in their concrete cores; this is due to the reduction in their bending capacities. For example, the CBPDS-DF specimen filled with normal concrete (0% recycled aggregates) achieved a ductility index equal to 4.4, and this value reduced to 4.1 and 3.4 when the same specimen was filled with concrete mixture content 50% and 100%, respectively, of recycled aggregate.
Based on the available experimental results, the newly developed theoretical model reasonably predicted the nominal bending capacity of the composite CBPDS with an acceptable mean value (0.970) and standard deviation (3.6%).
Notably, further investigations are required for these composite CBPDS specimens concerning the influence of varied parameters and loading scenarios that have not yet been studied. The developed theoretical model needs further validation with more empirical and numerical data for improvement, in order to make it generally applicable to this type of composite beam-slab system (CFST beam carrying PDS slab system).